# Solution

```ECE2280
Homework #1
Fall 2011
1. Use:
ignore ro, |VBE|=0.7, β=100
VI = 20+0.001sin(20t)
For DC analysis, assume that the capacitors are open
(a) Solve for the DC currents:
a. IB
b. IE
c. IC
+
100Ω
100
1m
Vx ≠- 0
1mA
C3
(b) Solve for the DC voltages:
a. VB
b. VE
c. Vo
IC
I1
10V
100Ω
2k
4kΩ
Vo
16V
VB
Q1
C4
100m
1k
100m
VI 4kΩ
IB
(c) Prove or disprove the region of operation you assumed to
solve for your answers in (a) and (b)?
1
6kΩ
10k
2V 8V
Q2N3904
IE
6.7V
900
VE
4kΩ
6V
Rout
2. Use:
ignore ro, |VBE|=0.7, β=100
VI = 5+0.001sin(500t)
rπ1=2, 000 gm2=50mA/V, and IB2=12.5&micro;
&micro;A
For the following hybrid-π equivalent circuit below, find the following values:
(a) Rin (input resistance –ignore only the input source, Vsig and include all resistors at the base)
(b) Rout (output resistance-include all resistors at the collector{no load is connected})
Vo
(c) midband gain,
Vsig
2k
3kΩ
2kΩ
Vo
100Ω
Vsig
~
2kΩ
+
+
Vπ1
-
rπ1
gm1Vπ1
Vπ2
rπ2
6kΩ
1kΩ
gm2Vπ2
-
Rout
Rin
4kΩ
2
4kΩ
3kΩ
3. For the circuit shown below, draw the AC small-signal
signal equivalent circuit(use hybrid-π
hybrid or model T).
Make sure that everything is labeled in terms of the transistor number. (e.g. gm1, vπ2, etc.). Include ro for all
transistors. vsig=0.001sin(10t) AC. Assume all capacitors are shorted.
+15V
R4
vsig
R6
-15V
3
+9V
4. Use:
Vt=2V
kn’(W/L)=4mA/V2
λ=0
VI = 10+0.002sin(20t)
For DC analysis, assume that
the capacitors act as open
(d) Solve for the DC currents:
a. I1
b. ID
c. IS
ID
3k
2k
Vo
C3
VG
1m
VI
C4
+
~
(e) Solve for the DC voltages:
a. VG
b. VS
c. Vo
NMOS
1k
I1
VS
4V
2k
500Ω
IS
+
(f) Verify that the transistor is saturated.
R in
(g) State the DC bias point.
100m
1.7V
R out
500Ω
(h) Assuming that the transistor amplification Vo/VI = -7V/V. What is the total (AC and DC)
instantaneous output for Vo (VI value stated above).
4
5. Use:
Vt=2V
kn’(W/L)=3mA/V2
Vsig is an AC source
Transistor 1 has DC values: VGS=4V, ID=6mA
Transistor 2 has DC values: VGS=5.3V, ID=16.7mA
λ=0 (for all transistors)
For the following hybrid-π equivalent circuit, find the following values:
(a) Rin (input resistance –ignore the input source, Vsig)
(b) Rout (output resistance-ignore RL{no load is connected})
Vo
(c) midband gain,
Vsig
3MΩ
2kΩ
+
v sig
~
2MΩ
vgs1
g m1v gs1
1kΩ
+
1kΩ
vgs2
g m2 v gs2
Vo
R L = 1kΩ
1kΩ
R in
R out
5
6
6. For the circuit shown below, draw the AC small-signal equivalent circuit(use hybrid-π or model T).
Make sure that everything is labeled in terms of the transistor number. (e.g. gm1, vgs2, etc.). λ=0 for all
transistors. vsig=0.005sin(20t) AC. Assume all capacitors are closed for the AC circuit.
+15V
R3
R8
1mA
+10V
+ 1V
Vsig
M2
NMOS
C3
100m
NMOS
R6
R1
R7
M1
R2
R9
~
R4
+
5V
R 10
R5
-15V
7
C1
10m
7 (a) Design the cascode amplifier with 2 PMOS transistors for the current source(as shown in class or Fig.
7.11) at a current of 0.1mA with all devices operating at |Vov|=0.25V. All devices have |VA|=4V. Find gm1,
the output resistance of the amplifier, Ron, the output resistance of the current source, Rop, the overall output
resistance, Rout, and the voltage gain, Av.
(b) Use the same circuit with the following DC voltages: VIn=0.8V, VG2=1.2V, VG3=1.3V, VG4=1.7V, and
VDD=2.5V. If all devices are matched, that is kn1= kn2= kp3= kp4, and have equal |Vt|=0.5V, what is the
overdrive voltage at which the four transistors are operating(Note this is different from part (a))? What is the
allowable voltage range at the output?
(a)
(b)
8
8. Design the cascode amplifier that utilizes 2 PMOS transistors for the current source to have the following
specifications: gm1=2mA/V, and Av=-200V/V. Assume that the available fabrication process has
V’A=5V/&micro;m for both NMOS and PMOS devices and that &micro;nCox= 4&micro;pCox=400&micro;A/V2 . Use the same channel
length L for all devices and operate all four devices at |Vov|=0.2V. Determine the required channel length L,
the bias current I, and the W/L ratio for each of four transistors. Assume that suitable bias voltages have been
chosen, and neglect the Early effect in determining the W/L ratios.
9
9. A cascode current source formed of two pnp transistors for which β=50 and VA=5V supplies a current of
0.5mA. What is the output resistance?
10. The figures below show four possible realizations of the folded cascode amplifier. Assume that the BJTs
have β=100 and that both the BJTs and the MOSFETs have |VA|=5V. Let I=100&micro;A, and assume that the
MOSFETs are operating at |VOV|=0.2V. Assume the current sources are ideal. For each circuit determine,
Rin, Rout, and the gain Vo/VI. Comment on your results.
(a)
10
(b)
(c)
(d)
11
```